Nick Clegg was tonight facing renewed pressure over the budget when Britain's equalities watchdog warned of action if ministers failed to carry out a statutory assessment of the impact of spending cuts on vulnerable people.

As the deputy prime minister insisted that fairness lay at the heart of the coalition programme, the Equality and Human Rights Commission (EHRC) said it might censure the government unless ministers can prove they met a legal requirement to consider the impact of cuts on the poor.

Clegg found himself under pressure after the Institute for Fiscal Studies described the budget today as "clearly regressive". The respected and impartial thinktank said that welfare cuts mean working families on the lowest incomes were the biggest losers in the budget.

Clegg, who had praised the work of the IFS before and during the general election, described its report as "partial" and a "single snapshot" after it excluded the effects of cuts in corporation tax and a rise in capital gains tax, which mainly affects higher income groups. He argued that the report failed to take account of plans to shift workers off benefits into full-time jobs. "If you just look at who is receiving benefits, then in a sense you don't ask the most important question of all, which is how you can relieve poverty and make Britain fairer by getting people off benefits and into work."

Clegg added that the government's plans also included a "pupil premium" to improve education opportunities for poorer children and further changes to the tax system. "That is a plan for real fairness, that is progressive. And I think that is a richer understanding of what fairness is about than a single snapshot that simply doesn't provide the full picture of what we are trying to do over the coming months and years."

Neil Kinghan, the EHRC's director general, issued his warning after Mark Hoban, the Treasury minister, stonewalled questions on the Today programme about whether the government had carried out a statutory assessment of the impact of the budget on women, ethnic minorities, disabled people and the elderly.

Kinghan said: "It is for the Treasury to demonstrate it has complied with legislation and assessed the impact of its decisions on vulnerable groups. If it cannot do so, then the commission will have to consider appropriate enforcement action."

Alistair Darling, the shadow chancellor, said: "Nick Clegg is talking nonsense. This is the man that promised we would 'see the stamp of Liberal Democrat values' all over the budget. It's not clear whether he was referring to the decision to hit the poorest hardest or to the singling out of families with children as the biggest losers. He might think he can take his party for fools, but the British public can see all too clearly that there's nothing fair about this coalition."